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Let R {\displaystyle R} be an integral domain and P {\displaystyle P} a prime ideal in R {\displaystyle R} . Consider a primitive polynomial:
f ( x ) = r 0 x n + r 1 x n − 1 + … + r n − 1 x + r n {\displaystyle f(x)=r_{0}x^{n}+r_{1}x^{n-1}+\ldots +r_{n-1}x+r_{n}}
where r 0 ∉ P {\displaystyle r_{0}\notin P} , r 1 , r 2 , … , r n ∈ P {\displaystyle r_{1},r_{2},\ldots ,r_{n}\in P} and r n ∉ P 2 {\displaystyle r_{n}\notin P^{2}} , then f {\displaystyle f} is an irreducible polynomial.
